In order to restore a computed tomogram, measurements of X-ray beams passing through a subject are reduced into a line integral, which in turn is inversely transformed into a projection function which represents attenuation coefficients of the subject.
Although monochromatic irradiation is required to obtain accurate values, all tomography instruments in the related art employ multi-chromatic irradiation in practice. Since tomograms reconstructed by multi-chromatic irradiation include strong artifacts, it is very difficult to calculate accurate line integrals of attenuation coefficients and to obtain accurate values of nonlinear problems provided by inverse transformation of an X-ray projection function.
A solution to such artifacts can be obtained by dual-energy tomography. In dual-energy tomography, the same subject is subjected to bi-chromatic irradiation with different energy levels. Images obtained through dual-energy tomography include fewer beam hardening artifacts.
An X-ray projection function of two spectra by dual-energy tomography is represented by simultaneous line integral equations of attenuation coefficients, and the measurements of X-ray beams detected in the two different spectra are substituted into the simultaneous equation to obtain line integral values.
These simultaneous equations are nonlinear equations as mentioned above, and polynomial approximation is generally used to solve the nonlinear equations. However, polynomial approximation doesn't provide accurate values of the equations. Moreover, it is also problematic in that irradiation and measurements of X-ray beams for calibration are required several times to obtain coefficients of the polynomials.
One example of the related art is disclosed in Korean Patent Publication No. 10-2001-0006602 (Publication date: Jan. 26, 2001) entitled “Apparatus and method for computed tomography”.